Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Invariant operators and univalent functions


Author: Reuven Harmelin
Journal: Trans. Amer. Math. Soc. 272 (1982), 721-731
MSC: Primary 30C55; Secondary 30C60
DOI: https://doi.org/10.1090/S0002-9947-1982-0662063-1
MathSciNet review: 662063
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions for univalence of meromorphic functions in certain domains in the complex plane are established in terms of some differential operators of degrees $ \ge 3$, possessing the same invariance property as the Schwarzian derivative. Those operators include the derivatives of the Schwarzian derivative and Aharonov's invariants. Conditions for the existence of quasiconformal extensions are also achieved.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30C55, 30C60

Retrieve articles in all journals with MSC: 30C55, 30C60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0662063-1
Article copyright: © Copyright 1982 American Mathematical Society